\(B=3^3+3^4+................+3^{61}+3^{62}\)(60 số hạng)
\(\Rightarrow B=\left(3^3+3^4+3^5\right)+\left(3^6+3^7+3^8\right)+...................+\left(3^{60}+3^{61}+3^{62}\right)\)
(20 nhóm)
\(\Rightarrow B=3^3\left(1+3+3^2\right)+3^6\left(1+3+3^2\right)+...........+3^{60}\left(1+3+3^2\right)\)
\(\Rightarrow B=3^3.13+3^6.13+.............+3^{60}.13\)
\(\Rightarrow B=13\left(3^3+3^6+.....+3^{60}\right)⋮13\)
\(\Rightarrow\) Số dư khi B chia cho 13 là 0
Ta có
B = 33 + 34 + 35 + 36 + ... + 361+ 362 (60 số hạng)
B = (33 + 34 + 35) + ... + (360 + 361 + 362) (20 nhóm)
B = 33(1 + 3 + 32) + ... + 360(1 + 3 + 32)
B = 33.13 + 36.13 + ... + 360.13
B = 13(33 + 36 + ...+ 360) \(⋮\)13
=> B chia cho 3 dư 0
